7 A random variable \(X\) has the distribution \(\operatorname { Po } ( 2.4 )\).
- Find \(\mathrm { P } ( 2 \leqslant X < 4 )\).
- Two independent values of \(X\) are chosen.
Find the probability that both of these values are greater than 1 .
- It is given that \(\mathrm { P } ( X = r ) < \mathrm { P } ( X = r + 1 )\).
- Find the set of possible values of \(r\).
- Hence find the value of \(r\) for which \(\mathrm { P } ( X = r )\) is greatest.
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